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Solar activity undergoes a variation over time scales of several months knownas Rieger-type periodicity, which usually occurs near maxima of sunspot cycles.An early analysis showed that the periodicity appears only in some cycles, andis absent in other cycles. But the appearance/absence during different cycleshas not been explained. We performed a wavelet analysis of sunspot data fromthe Greenwich Royal Observatory and the Royal Observatory of Belgium duringcycles 14-24. We found that the Rieger-type periods occur in all cycles, butthey are cycle-dependent: shorter periods occur during stronger cycles. Ouranalysis revealed a periodicity of 185-195 days during the weak cycles 14-15and 24, and a periodicity of 155-165 days during the stronger cycles 16-23. Wederived the dispersion relation of the spherical harmonics of the magneticRossby waves in the presence of differential rotation and a toroidal magneticfield in the dynamo layer near the base of the convection zone. This showedthat the harmonic of fast Rossby waves with m=1 and n=4, where m (n) indicatethe toroidal (poloidal) wavenumbers, respectively, perfectly fit with theobserved periodicity. The variation of the toroidal field strength from weakerto stronger cycles may lead to the different periods found in those cycles,which explains the observed enigmatic feature of the Rieger-type periodicity.Finally, we used the observed periodicity to estimate the dynamo field strengthduring cycles 14-24. Our estimations suggest a field strength of 40 kG for thestronger cycles, and 20 kG for the weaker cycles.

Rieger-type periodicity during solar cycles 14-24: estimation of dynamo magnetic field strength in the solar interior